Least Common Multiple of 46 and 47

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

• Least Common Multiple of 46 and 47 by Prime method
• Least Common Multiple of 46 and 47 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 46 and 47. First we will calculate the prime factors of 46 and 47.

Prime Factorization of 46

Prime factors of 46 are 2,23. Prime factorization of 46 in exponential form is:

46 = 2¹×23¹

Prime Factorization of 47

Prime factors of 47 are 47. Prime factorization of 47 in exponential form is:

47 = 47¹

Now multiplying the highest exponent prime factors to calculate the LCM of 46 and 47.

LCM(46,47) = 2¹×23¹×47¹
LCM(46,47) = 2162

Factors of 46

List of positive integer factors of 46 that divides 46 without a remainder.

1, 2, 23, 46

Factors of 47

List of positive integer factors of 47 that divides 47 without a remainder.

1, 47

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46 and 47, than apply into the LCM equation.

GCF(46,47) = 1
LCM(46,47) = ( 46 × 47) / 1
LCM(46,47) = 2162 / 1
LCM(46,47) = 2162

(i) The LCM of 47 and 46 is associative

LCM of 46 and 47 = LCM of 47 and 46

1. What is the LCM of 46 and 47?

Answer: LCM of 46 and 47 is 2162.

2. What are the Factors of 46?

Answer: Factors of 46 are 1, 2, 23, 46. There are 4 integers that are factors of 46. The greatest factor of 46 is 46.

3. What are the Factors of 47?

Answer: Factors of 47 are 1, 47. There are 2 integers that are factors of 47. The greatest factor of 47 is 47.

4. How to Find the LCM of 46 and 47?

Answer:

Least Common Multiple of 46 and 47 = 2162

Step 1: Find the prime factorization of 46

46 = 2 x 23

Step 2: Find the prime factorization of 47

47 = 47

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2162 = 2 x 23 x 47

Step 4: Therefore, the least common multiple of 46 and 47 is 2162.